The linear solver step in aggregated finite element methods has been studied in [1]}. The authors propose a row-wise linear algebra distribution layout for the resulting matrix in [1]} and minimize the amount of inter-processor communications. The authors use the parallel implementation of aggregated finite elements in \(\mathtt {FEMPAR}\)  [3]}. They apply a standard algebraic multigrid preconditioner (called \(\mathtt {GAMG}\) ) from the \(\mathtt {PETSc}\)  library [4]} using a standard configuration. The results in [1]} show excellent scalability and optimality properties for this standard solver applied to the aggregated finite element method. The aggregated results are very similar to the results obtained with boundary-fitted meshes. The largest problems that are considered exceed \(10^9\)  elements on 16,464 processors. From these numerical experiments, it is observed that the additional coupling between boundary degrees of freedom does not affect a standard algebraic multigrid preconditioner.
